Thursday, 12 July 2018

Oh, the places you’ll go!

In economics, the cost-benefit principle is the idea that a rational decision-maker will take an action if, and only if, the incremental (extra) benefits from taking the action are at least as great as the incremental (extra) costs. We can apply the cost-benefit principle to find the optimal quantity of things (the quantity that maximises the difference between total benefits and total costs). When we do this, we refer to it as marginal analysis.

Marginal analysis challenges the idea that we are always better off with more of things. Yes, we might like there to be more white rhinos, but if there was one living in every front yard, we'd probably regret it. More is not always better.

The easiest way to understand marginal analysis is to see it in action. A recent article in The Economist provides us with a good example:
When it comes to habitat, human beings are creatures of habit. It has been known for a long time that, whether his habitat is a village, a city or, for real globe-trotters, the planet itself, an individual person generally visits the same places regularly. The details, though, have been surprisingly obscure. Now, thanks to an analysis of data collected from 40,000 smartphone users around the world, a new property of humanity’s locomotive habits has been revealed.
It turns out that someone’s “location capacity”, the number of places which he or she visits regularly, remains constant over periods of months and years. What constitutes a “place” depends on what distance between two places makes them separate. But analysing movement patterns helps illuminate the distinction and the researchers found that the average location capacity was 25. If a new location does make its way into the set of places an individual tends to visit, an old one drops out in response. People do not, in other words, gather places like collector cards. Rather, they cycle through them. Their geographical behaviour is limited and predictable, not footloose and fancy-free.
When it comes to the number of locations we visit, there appears to be an optimal number and that optimal number is 25. Why? Consider the costs and benefits of adding one more location to the number that you regularly visit. We can refer to those costs and benefits as marginal costs and marginal benefits. When economists refer to something as marginal, you can think of it as being associated with one more unit (in this case, associated with one more location that you regularly visit).

The marginal benefit of locations declines as you add more locations to your regular routine. Why is that? Not all locations provide you with the same benefit, and you probably go to the most beneficial places most often. So naturally, the next location you add to your regular routine is going to provide less additional benefit (less marginal benefit) than all of the other locations you already visit regularly. So, as shown in the diagram below, the marginal benefit (MB) decreases as you include more locations in your routine.

The marginal cost of locations increases as you add more locations to your regular routine. Why is that? Every location you choose to go to entails an opportunity cost - something else that you have given up in order to go there. When you add a new location to your routine, you are probably giving up spending some time at one of the other locations you were already going to, which provide you with a high benefit. The more locations you add, the more you need to cut into your time at high-benefit locations. So, as shown in the diagram below, the marginal benefit (MC) increases as you include more locations in your routine.

The optimal number of locations occurs at the quantity of locations where marginal benefit exactly meets marginal cost (at Q*). If you regularly visit more than Q* locations (e.g. at Q2), then the extra benefit (MB) of visiting those locations is less than the extra cost (MC), making you worse off. If you regularly visit fewer than Q* locations (e.g. at Q1), then the extra benefit (MB) of visiting those locations is more than the extra cost (MC), so visiting one more location would make you better off.

And, it turns out, the optimal number of locations (Q*) is limited to roughly 25.

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